Li 2(z)+Li 2(1-z)=pi^2/6-log(z)log(1-z)

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Theorem

The following formula holds: $$\mathrm{Li}_2(z)+\mathrm{Li}_2(1-z)=\dfrac{\pi^2}{6} - \log(z)\log(1-z),$$ where $\mathrm{Li}_2$ denotes the dilogarithm, $\pi$ denotes pi, and $\log$ denotes the logarithm.

Proof

References